Electricity

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Electricity

• Electricity
• Updated 2/7/07

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Electricity

• This section will discuss electricity and
  electric circuits, and will be followed by a
  section on magnetism.
• Electricity will begin with a discussion of
  electric charges and the forces between them,
  sometimes called electrostatics, then move on to
  electric potential and current.

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Electricity

• electrostatics electricity at rest. Includes
  electric charges, the electrostatic forces
  between them, and their behavior in materials.
• Electric charges can be positive or negative and
  are measured in Coulombs (C).
• The minimum possible charge is the charge on an
  electron (-) or a proton ().

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Electrostatics
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Electricity

• Coulombs Law
• F k q1 q2
• ______________________
• r2
• where F force in newtons (N)
• q charge in Coulombs (C)
• r distance between charges (m)
• k 9.0 x 109 N?m2/C2

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Electricity

• Coulombs Law (alternate form)
• F q1 q2
• _________________________
• 4p?0r2
• where k 1 / 4p?0 and
• ?0 permittivity of free space

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Electricity

• Charges are always an integer multiple of the
  charge of an electron. The electron charge can
  not be subdivided into smaller charges.

A Coulomb is about the same as the charge on 6.24
x 1018 electrons.
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Electricity
Millikan Oil-Drop Experiment

• Measured the elementary charge, e
• Found that every charge was an integral multiple
  of e
• q n e

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Electricity

• The forces resulting from electrical charges is
  many, many times stronger than the forces of
  gravitational attraction.
• Protons are positively charged. Electrons have a
  negative charge. Neutrons have no charge.
• Opposite charges result in an attractive force,
  like charges in a repelling force.

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Electricity
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Electricity

• Opposite charges result in an attractive force,
  like charges in a repelling force.

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Electricity

• Definitions
• conservation of charge electric charge is
  neither created nor destroyed, but may be
  transferred between materials.
• There are three ways of transferring charge
• friction
• contact
• induction.

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Electricity

• One way to charge an object is by friction, that
  is, transferring electrons from one object to
  another by rubbing (balloon and hair, shoes and
  rug).
• Examples balloon and hair
• glass rod and cloth
• leather shoes and carpet
• silk and nylon

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Electricity

• Story Time!
• IBM Computer
• Gas Station Fire
• Dangerous Dating
• Spark Wars
• (Fingers, Coins and Hangers)
• Deadly Doorknobs
• Go to Ground!

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Electricity

• A second way to charge an object is by contact or
  conduction, that is, to touch an uncharged object
  with a charged object.
• Examples balloon and electroscope, Van de Graf
  generator, rechargeable batteries.

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Electricity

• A third way to charge an object is by induction.
  This method requires only that a charged object
  be brought close to an uncharged object, inducing
  a separation of charges.
• Examples balloon and electroscope
• thunderstorms

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Electricity

• With induction, the induced charge on an object
  can be maintained by grounding the repulsed
  charge.

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Electricity

• Some molecules, such as water, are naturally
  electrically polarized, that is, the positive
  charge from the hydrogen is concentrated on one
  side of the molecule and the negative charge from
  the oxygen is on the other side. Water thus
  forms a molecule known as an electric dipole.

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Electricity

• Grounding is a way to bring the charges back into
  balance by allowing the excess charges to bleed
  off into the environment.
• Examples balloon and electroscope
• lightning rods
• doorknobs

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Electricity

• Definitions
• conductors materials (such as metals like
  copper and gold) with free electrons that allow
  electric charges to be easily carried from one
  place to another.
• insulators materials (such as rubber) that are
  poor conductors of electric charge.

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Electricity

• Definitions
• semiconductors materials (such as silicon) that
  exhibit the traits of conductors and insulators,
  depending on conditions.
• superconductors materials that are perfect
  conductors and have a zero resistance to the flow
  of charge.

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Electricity

• Electric Fields
• Electric fields are a vector quantity. If there
  are more than two charges, the overall force can
  be calculated using vector addition.
  (Superposition Principle)
• All of the electric field equations assume that
  the reference charge is positive and small in
  comparison with the measured charge

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Superposition Principle Example

• For 2 charges with the same sign
• The force exerted by q1 on q2 is F12
• The force exerted by q2 on q1 is F21
• If the charge signs are different, the force is
  reversed in direction.

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Superposition Principle Example

• The force exerted by q1 on q3 is
• The force exerted by q2 on q3 is
• The total force exerted on q3 is the vector sum
  of
• and

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Superposition Principle Example

• The force exerted by q1 on q3 is
• The force exerted by q2 on q3 is
• The total force exerted on q3 is the vector sum
  of
• and

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Electricity

• Electric Fields
• At any point in a field, the direction of the
  field is represented by the direction of the
  field lines closest to that point, and the
  magnitude of the field is represented by the
  number of field lines passing close to that
  point.

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Electricity

• The electric field E is the force per positive
  unit test charge
• E F / qt
• where qt is the test charge,
• then by Coulombs Law
• F (kq1qt) / r2
• ? E (kq1) / r2

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Electricity

• Induction is evidence that space around charged
  objects is filled with electric fields. Here are
  the radial fields associated with point charges.

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Electricity
A test charge placed between the two charges
will move in a straight line from Q to -Q. If
the test charge is placed elsewhere, the possible
paths change.
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Electricity
For a test charge placed near the Q charges,
the possible paths are shown below. (The
direction of the arrows changes if the charges
are changed to -Q.)
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Electricity
On an irregularly shaped conductor, the charge
accumulates at locations where the radius of
curvature of the surface is smallest (that is, at
the sharp points where the curvature is greatest).
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• excess charge moves to the surface
• charges move apart until equilibrium is achieved
• the charge per unit area is greater at the flat
  end
• forces at the sharp end produce a larger
  resultant force away from the surface
• this is how a lightning rod works

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Electricity
For parallel plates, the movement of a test
charge is shown below. Note the bulge in the
outside lines.
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Electricity

• Definitions
• capacitor a common device used to store
  electrical energy that is composed of two
  conducting plates separated by an insulator. The
  plates are charged by connecting them to source
  of opposite charge, such as a battery.

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Electricity

• Definition
• electric potential energy work is done if you
  move a charged object against an electric field,
  creating electric potential energy.
• Example If you move a positively charge object
  closer to another positively charged object, you
  do work and create electric potential energy.

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Electricity

• Electric Potential Energy
• Since we defined the electric field E to be the
  force per unit charge
• E F / q
• we can also say the converse is true, i.e. the
  force F is equal to the field times the unit
  charge.
• F (q E)

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Electricity

• Electric Potential Energy
• Now by the work-energy theorem, the change in the
  electric potential energy is also equal to the
  work done to move a charged particle in an
  electric field. Work is force times distance
• ?PE Work F d
• and since F (q E)
• F d (q E) d

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Electricity

• Where there is a uniform field between two flat
  plates, then when a charge moves a distance d
  xf xi from A to B, work is done on it.
• W F d (q E) d
• and ?PE - W
• ? ?PE - (q E) d
• only for a uniform field

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Electricity

• electric potential a measure of the electric
  potential energy per unit charge.
• electric potential PE
• q
• electric potential is commonly known as voltage.
  The unit of electric potential is the volt.
• volt joule
• coulomb

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Electricity

• Reprise
• Combining the ideas in the last two slides
• The potential difference between points A and B
  is defined as the change in the potential energy,
  (final value minus initial value), of a charge q
  moved from A to B divided by the size of the
  charge
• ?V VB VA ?PE / q

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Electricity

• Reprise II
• Rearranging the last equation gives us
• ?PE q ?V
• Both electric potential energy and potential
  difference are scalar quantities, the work done
  to move a charge from one point to another is
  independent of the path taken.
• Units of potential difference V J/C

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Electricity

• Using the last two definitions
• ?PE F d
• ?PE q ?V
• and since F q E
• F d (q E) d q ?V
• canceling out the q E d ?V

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Electricity

• Electric Potential Energy
• If we release a charge that has electric
  potential energy, that charge will accelerate and
  convert the potential energy to kinetic energy.
• PE (q E) d ½mv2 KE
• ? v (2 (q E d) / m)½

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Electricity

• Electric Potential Energy
• Since the d in the equation below is the same
  as r in Coulombs Law
• PE (q E) d (q E) r
• PE (q E) d (F) r ((kq1q2) / r2 ) r
• ? PE (kq1q2) / r

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Electricity

• electronvolt the unit used by physicist for
  very small energies, equivalent to the energy
  gained by an electron moving through a potential
  difference of 1 volt.
• electronvolt 1 volt x 1.6 x 10-19 C
• electronvolt 1.6 x 10-19 J

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Electricity

• Current Flow
• Where there is a difference in potential
  (voltage), a current will flow until both ends
  reach a common potential. When there is no
  potential difference, there is no current flow.
• Electric current is simply the flow of an
  electric charge.

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Electricity

• Current Flow
• Whenever charges move, that is termed a current.
  The path they follow is a circuit.
• I Q / t
• In other words, current is the rate at which
  charge passes a given point.
• According to convention, current is a flow of
  positive charges. (Actually, its the negative
  electrons that move.)

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Electricity

• Current Flow
• As the electrons move, they bump into each other
  and atoms. This slows the electrons down, and
  work is done. This process heats up the
  conductor. The speed of the electron flow
  through the conductor is called the drift
  velocity.

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Electricity

• Current Flow
• ampere (amp) the unit of electric current,
  designated by the SI unit A, equal to the flow
  of 1 coulomb of charge per second.
• Example A wire carrying a 5 A current will have
  5 coulombs of charge pass a point each second.
  (The wire itself does not have a charge.)

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Electricity

• Ohms Law
• Ohms Law describes the relationship between
  the fundamental electric qualities of voltage,
  current and resistance.
• current voltage
• resistance

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Electricity

• Ohms Law
• 1 ampere (I) 1 volt (V)
• ohm (R)
• therefore 1 ohm 1 volt
• 1 ampere
• I V/R is often written as V IR

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Electricity

• Ohms Law
• ohmic devices that obey Ohms Law.
• Ohms Law assumes that the temperature remains
  constant. An ohmic device with a constant
  resistance is a resistor.
• Devices like lamps, whose resistance changes with
  temperature are non-ohmic.

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Electricity

• Ohmic Device
• The resistance is constant over a wide range of
  voltages
• The relationship between current and voltage is
  linear
• The slope is related to the resistance

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Electricity

• Non-Ohmic Device
• Non-ohmic materials are those whose resistance
  changes with changes in voltage or current
• The current-voltage relationship is nonlinear
• A filament lamp is a common example of a
  non-ohmic device

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Electricity

• Ohms Law and Shocks
• It aint the voltage that kills you, its the
  current!!! Ohms law applies to sticking your
  fingers in a light socket, as well as many other
  situations.

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Electricity

• Shocking! If your body is at its normal dry
  resistance of about 100,000 ohms

If your body is damp and you are barefoot, your
resistance may be as low as 1,000 ohms
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Electricity

• Direct and Alternating Current
• direct current (DC) a steady flow of electrons
  in one direction.
• Batteries and solar cells provide this kind of
  current. DC is used to power computers,
  calculators, toys and is the type of current in
  your car. Ohms law applies to DC.

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Electricity

• Direct and Alternating Current
• Most electronic circuits use low voltage DC. For
  instance, most computers use 5 volt and 15 volt
  power, with the CPU needing only 5 volts.
• DC circuits are easy to design, but electric
  transmission is inefficient. (Tesla)

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Electricity

• Direct and Alternating Current
• alternating current (AC) a back and forth flow
  of electrons. The voltage cycles from plus to
  minus 60 times per second.
• This is the standard for power transmission in
  the US. AC is produced by generators and used by
  light bulbs, stoves, fans, etc.

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Electricity

• Direct and Alternating Current
• Most power plants produce three phase A/C power.
  Lights and home appliances in the U.S. use either
  110 volts or 220 volts.
• AC circuits are difficult to design, but electric
  transmission is efficient. (Edison) Special
  converters change AC to DC for use in electronic
  devices.

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Electricity

• Electric Power
• electric power the rate at which electric
  energy is converted into another form, such as
  mechanical energy, heat or light.
• electric power current x voltage
• 1 watt 1 ampere x 1 volt

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Electricity

• Electric Power
• electric power voltage x current
• P V I
• since V I R
• P I ( I R ) I2 R

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Electricity

• End of Electricity